Saturday, February 07, 2015

State IQ estimates, whites only (2013)

IQ estimates similarly arrived at through the utilization of 2013 NAEP results in math and reading among white 8th graders follow. The scores for both tests are on a 500 point scale, with a designed standard deviation of 50. In the proceeding table, these are converted into IQ estimates with a mean of 97.4--corresponding to the national average NAEP scores of 283.62 for math and 266.02 for reading--and a standard deviation of 15. The math and reading scores are given equal weighting.

In the spirit of the 2004 IQ hoax, states are color-coded according to how their white electorates voted in 2012. Due to insufficient exit polling data in the less competitive states, it's not possible to accurately ascertain the margins of victories among whites at the state level, so red (blue) indicates a simple Romney (Obama) win. Connecticut split evenly, 49%-49%:

State

IQ

1. District of Columbia

108.0

2. Massachusetts

104.4

3. New Jersey

103.5

4. Maryland

103.0

5. Connecticut

102.4

6. Colorado

102.3

7. Minnesota

102.2

8. Texas

102.1

9. Pennsylvania

102.1

10. Washington

101.7

DoDEA

101.7

11. Illinois

101.4

12. New Hampshire

101.4

13. New York

101.3

14. Vermont

101.1

15. Delaware

101.1

16. Virginia

101.1

17. Montana

100.9

18. Wisconsin

100.9

19. North Carolina

100.9

20. Rhode Island

100.9

21. Hawaii

100.8

22. Ohio

100.8

23. Alaska

100.7

24. Nebraska

100.7

25. Kansas

100.6

26. California

100.4

27. South Dakota

100.3

28. Georgia

100.3

29. Florida

100.3

30. Arizona

100.2

31. Indiana

100.2

32. North Dakota

100.1

33. Idaho

100.0

34. Oregon

100.0

35. Utah

99.8

36. South Carolina

99.8

37. Missouri

99.8

38. Wyoming

99.7

39. Iowa

99.6

40. New Mexico

99.5

41. Nevada

99.5

42. Maine

99.3

43. Michigan

99.1

44. Kentucky

99.0

45. Louisiana

98.9

46. Tennessee

98.7

47. Arkansas

98.4

48. Mississippi

98.2

49. Oklahoma

97.7

50. Alabama

97.5

51. West Virginia

95.1

For the uninitiated who feel as though they're seeing an awful lot of red in the preceding table and presume I'm in error giving vermilion hues to the likes of California, Illinois, and New Jersey, please do see here.

Texas outperforms expectations. Is it something miraculous or is something awry? Whatever the case, the state is going to sink under the weight of its increasing diversity load so that even if each of its ethnic groups continue to outperform the expectations of their respective groups, the state as a whole is going to slip into the bottom third of states in the next decade or so.

Notice that the estimates show a mean IQ value above 100 (100.7 to be precise). It's an artifact of my presumption that the national average for the US is 98, the figure given in IQ and the Wealth of Nations, published in 2002 (with national estimates based on data obviously older than that). As the US steadily becomes less white, the national average will correspondingly decline. That should already be the case in 2015, and it's detectable here. Working backwards, I'd peg the contemporary US average at 97.

"One disadvantage of portraying NAEP results in terms of scaled scores is that the scaling metric is arbitrary. Until very recently, all of the NAEP scales used values that ranged from a minimum score of zero to a maximum score of 500 across the three grade levels tested (grades 4, 8, and 12 in the most recent assessments). In the base year, each scale had a mean of 250.5 and a standard deviation of 50 points (Linn and Dunbar 1992). Although the use of an arbitrary scale metric is common in educational testing (for example, the Scholastic Assessment Tests and the Graduate Record Examinationsmake use of subtest scales that, when introduced, had a mean of 500 and a standard deviation of 100), users have difficulty determining the importance of given scale scoredifferences until such scales have been used for a number of years. For example, is a five-point difference in mean scale score from one NAEP assessment to the next an important difference or a trivial difference in terms of educational importance? Notsurprisingly, this question still has not been answered satisfactorily for NAEP. As a result, NAEP reports focus on the statistical significance of the differences between mean NAEPscores for various subpopulations or on the statistical significance of changes in mean NAEP scores, across assessments, for a given population or subpopulation."

The means and SDs fluctuate from year to year. The means have crept upwards towards 500 over the years and partly as a consequence the mean SDs have shrunk some. It's the relative rankings that are of more interest. If we want to presume a SD of 40 instead of 50 for all the states, multiply the difference between 98.0 by .8 for each result.

I'm going to assume we're seeing the 60th %ile (or perhaps close to it, thanks to racial confounding) for Texas, rather than the mean. If so, the true mean is 98.3, which is a much more believable number and fits in geographically quite perfectly.

"For the uninitiated who feel as though they're seeing an awful lot of red in the preceding table and presume I'm in error giving vermilion hues to the likes of California, Illinois, and New Jersey, please do see here."

I think extreme caution should be applied when looking at the exit polls. Consider New Jersey. In 2008, McCain supposedly won whites there by 1 point, while in 2012 Romney won whites by 13%, which was counterbalanced by an increase in the share of the non-white vote...

...except the data don't support this story. Obama's performance in almost very heavily white Republican strongholds was basically unchanged from 2008 to 2012. These areas have been become more Hispanic, but not by nearly enough to explain the non-trend. My feeling is that the demographic projections for exit polls are done by people who don't really know what they're doing, but that people who do ignore it, because it's fun to work with the numbers as though they're real.

In 2006, I did the same thing using 2005 numbers, a few months before McDaniel's released his. He used science and reading instead of math and reading, and, not surprisingly, our results correlated almost perfectly, at over .96.

Nooffensebut,

Any chance you'd send me the xml file of the composite scores by state? crush41@iwon.com

Without weighting by population that doesn't tell you much of anything. The standard deviation estimate is taken from the NAEP score distributions among all participating students. What you're seeing here is that the average (mean) white student in West Virginia falls at around the 35th percentile of the national average (mean).

That makes sense now, but I'm still trying to get my head around what the sample sd means. It is true that in your data, the Massachusetts average is almost 4 sds higher than the Mississippi average, but I guess that means nothing…

I’m finding your data fascinating and confirming some construct validity issues I had with my data (using McDaniel’s estimates). An example in my data, the correlation between state IQ and openness to experience is exactly zero. When controlling for %black and Hispanic, it’s .29. In your data, the correlation is simply .32. Makes sense.

Another example, your IQ scores correlate far less strongly with state temperature (-.27) than mine do (-.48; even after I control for race—it’s -.66 before race control).

Also, I’m not at all a hippie liberal trying to start a fight, but any comment on the blue state advantage?

I hope this isn’t a can of worms, but someone tells me my interpretation of the SD is correct. So, I clicked on your NAEP link, showing math scores. I used only the 50 states and calculate a mean of 292.18 with a standard deviation of 6.02.

Massachusetts has a mean of 307.47. Subtract out 292.18 and divide by 6.02. Massachusetts’ Z score is 2.54. Mississippi has a mean of 284.78. Subtract out 292.18 and divide by 6.02. Mississippi’s Z score is -1.23. The states differ in “relative average math iq” by 3.77 standard deviations. These are obviously aggregates based on large samples of students within states…

If we used a true IQ metric, we would take 97.4 (your mean estimate for the USA—versus 100—relative to the rest of the world) and then multiply each state’s Z score by 15. Thus, Massachusetts’ relative IQ = 135.5. And, Mississippi’s is 78.95. The difference is staggering and seems untenable, which led some to decide not to scale the scores with a SD of 15. Unless I’m missing something then, your values are not scaled in the traditional IQ metric.

To wit, note that in your NAEP link, Massachusetts (first place; your IQ estimate is 104.4) is significantly smarter than New Jersey (second place; your IQ estimate is 103.5). Yet the difference using your metric is only 0.9 IQ points? Thus, however it’s reported, with the 50 states as the unit of analysis, Massachusetts averages 3.77 SDs higher than does Mississippi (56.6 IQ points!).

Any counter argument to the above would be most appreciated (happy to be proven wrong; this issue has bugged the hell out of me for about 5 years…).

What I think you're doing is treating the 50 state list as though it is a sample population with an N of 50 and then calculating a standard deviation based on a normal distribution for those 50 values. The distribution of 50 state means values is going to be much narrower than the range of scores across a national population sample. Along the lines of the Lewontin fallacy, there is more variation in scores within a state than there is across states but that shouldn't insinuate that the differences between state averages are meaningless.

I'm not sure if you're able to calculate standard deviation for the national sample populations with the data available on NAEP's site (although I'm not sure as I'm emphatically not a statistician). The site does provide some SD values. Originally the test was designed to target 50 points as a SD on a 500 point scale but the realized SDs have been smaller than that for almost 20 years now. I'm going to use a standard deviation of 40 instead of 50 when I tweak the numbers (that won't have an effect on any correlations that are done with them, though, because it's going to be a uniform change across scores).

As for the blue state population advantage, I've looked at that in a lot of different ways. White liberals do consistently score higher on cognitive tests than white conservatives do. The left has trouble celebrating this though because when non-whites are included, liberals and conservatives are basically indistinguishable and Republicans consistently outscore Democrats.